eigenBootParallel {nFactors}

Bootstrapping of the Eigenvalues From a Data Frame

Description

The eigenBootParallel function samples observations from a data.frame to produce correlation or covariance matrices from which eigenvalues are computed. The function returns statistics about these bootstrapped eigenvalues. Their means or their quantile could be used later to replace the eigenvalues inputted to a parallel analysis. The eigenBootParallel can also compute random eigenvalues from empirical data by column permutation (Buja and Eyuboglu, 1992).

Usage

eigenBootParallel(x, quantile = 0.95, nboot = 30,
  option = "permutation", cor = TRUE, model = "components", ...)

Arguments

x

data.frame: data from which a correlation matrix will be obtained

quantile

numeric: eigenvalues quantile to be reported

nboot

numeric: number of bootstrap samples

option

character: "permutation" or "bootstrap"

cor

logical: if TRUE computes eigenvalues from a correlation matrix, else from a covariance matrix (eigenComputes)

model

character: bootstraps from a principal component analysis ("components") or from a factor analysis ("factors")

...

variable: additionnal parameters to give to the cor or cov functions

Value

values

data.frame: mean, median, quantile, standard deviation, minimum and maximum of bootstrapped eigenvalues

Author(s)

Gilles Raiche
Centre sur les Applications des Modeles de Reponses aux Items (CAMRI)
Universite du Quebec a Montreal
[e-mail]

References

Buja, A. and Eyuboglu, N. (1992). Remarks on parallel analysis. Multivariate Behavioral Research, 27(4), 509-540.

Zwick, W. R. and Velicer, W. F. (1986). Comparison of five rules for determining the number of components to retain. Psychological bulletin, 99, 432-442.

See Also

principalComponents, iterativePrincipalAxis, rRecovery

Examples

# .......................................................
# Example from the iris data
 eigenvalues <- eigenComputes(x=iris[,-5])

# Permutation parallel analysis distribution
 aparallel   <- eigenBootParallel(x=iris[,-5], quantile=0.95)$quantile

# Number of components to retain
 results     <- nScree(x = eigenvalues, aparallel = aparallel)
 results$Components
 plotnScree(results)
# ......................................................

# ......................................................
# Bootstrap distributions study of the eigenvalues from iris data
# with different correlation methods
 eigenBootParallel(x=iris[,-5],quantile=0.05,
                   option="bootstrap",method="pearson")
 eigenBootParallel(x=iris[,-5],quantile=0.05,
                   option="bootstrap",method="spearman")
 eigenBootParallel(x=iris[,-5],quantile=0.05,
                   option="bootstrap",method="kendall")